A primal feasible active set method is presented for finding the unique solution of a Linear Complementarity Problem (LCP) with a P-matrix, which extends the globally convergent active set method for strictly convex quadratic problems with simple bounds proposed by [P. Hungerlaender and F. Rendl. A feasible active set method for strictly convex problems with … Read more
Low-rank tensor methods provide efficient representations and computations for high-dimensional problems and are able to break the curse of dimensionality when dealing with systems involving multiple parameters. We present algorithms for constrained nonlinear optimization problems that use low-rank tensors and apply them to optimal control of PDEs with uncertain parameters and to parametrized variational inequalities. … Read more
We propose primal-dual active-set (PDAS) methods for solving large-scale instances of an important class of convex quadratic optimization problems (QPs). The iterates of the algorithms are partitions of the index set of variables, where corresponding to each partition there exist unique primal-dual variables that can be obtained by solving a (reduced) linear system. Algorithms of … Read more